The Information Theory of Developmental Pruning: Optimizing Global Network Architecture Using Local Synaptic Rules

Another paper from the Hennig lab is out, this one is from Carolin Scholl's master's thesis. Once again, we used an artificial neural network to get intuition about biology. The paper is on BioRiv, and you can also get the PDF here. 

Stable task information from an unstable neural population

In this paper, we test one of the hypothesis from the "Causes and consequences of representational drift" review: that neural population codes might support a stable readout, even as single neural tunings reconfigure. 

[get PDF]

We examined long-term neuroimaging recordings form Driscoll et al. (2017). We found that the population code does, indeed, preserve a stable readout over time. This is because much of the reconfiguration in the neural code is orthogonal to the directions that encode behavior. 

Even this readout isn't perfectly stable, however, so some amount of ongoing compensation must occur to allow readouts to adjust to the shifting neural code. This residual reconfiguration is much slower than the apparent day-to-day variability in single neurons, so it could be easily tracked with synaptic plasticity. 

Many thanks to all! This really was a team effort: data were collected by Laura Driscoll and colleagues in the Harvey lab, and most of the analysis was started by Adriana Loback. Dhruva Raman was instrumental in sorting out the null model simulations. The paper can be cited as

Rule, M.E., Loback, A.R., Raman, D.V., Driscoll, L.N., Harvey, C.D. and O'Leary, T., 2020. Stable task information from an unstable neural population. Elife, 9, p.e51121.

Excerpt: Figure 4

A slowly-varying component of drift disrupts the behavior-coding subspace. (a) The small error increase when training concatenated decoders (Figure 3) suggests that plasticity is needed to maintain good decoding in the long term. We assess the minimum rate for this plasticity by training a separate decoder Md for each day, while minimizing the change in weights across days. The parameter λ controls how strongly we constrain weight changes across days (the inset equation reflects the objective function to be minimized; Methods). (b) Decoders trained on all days (cyan) perform better than chance (red), but worse than single-day decoders (ochre). Black traces illustrate the plasticity-accuracy trade-off for adaptive decoding. Modest weight changes per day are sufficient to match the performance of single-day decoders (Boxes: inner 50% of data, horizontal lines: median, whiskers: 5–95th%). (c) Across days, the mean neural activity associated with a particular phase of the task changes (Δμ). We define an alignment measure ρ (Materials and methods) to assess the extent to which these changes align with behavior-coding directions in the population code (blue) verses directions of noise correlations (ochre). (d) Drift is more aligned with noise (ochre) than it is with behavior-coding directions (blue). Nevertheless, drift overlaps this behavior-coding subspace much more than chance (grey; dashed line: 95% Monte-Carlo sample). Each box reflects the distribution over all maze locations, with all consecutive pairs of sessions combined.

Causes and consequences of representational drift

Drs. Harvey, O'Leary, and myself, have just published a review in Current Opinion in Neurobiology titled the "Causes and consequences of representational drift" [PDF].

We explore recent results from the work of Alon Rubin and Liron Sheintuch in the Ziv lab and Laura Driscoll in the Harvey lab. Their work has shown that neural representations reconfigure even for fixed, learned tasks. 

We discuss ways that the brain might support this reconfiguration without forgetting what it has already learned. There might be a subset of stable neurons that maintain memories. Alternatively, neural representations can be highly redundant, and support a stable readout even as single cells seem to change. 

Finally, we conjecture that redundancy allows different brain areas to "error-correct" each other, allowing the brain to keep track of the shifting meaning of single neurons in plastic representations.

For a brief preview, here are the pre-publication versions of figures 2 and 3:

Figure 2:

Figure 2: Internal representations have unconstrained degrees of freedom that allow drift. (a) Nonlinear dimensionality reduction of population activity recovers the low-dimensional structure of the T-maze in Driscoll et al. (2017). Each point represents a single time-point of population activity, and is colored according to location in the maze. (b) Point clouds illustrate low-dimensional projections of neural activity as in (a). Although unsupervised dimensionality-reduction methods can recover the task structure on each day, the way in which this structure is encoded in the population can change over days to weeks. (c) Left: Neural populations can encode information in relative firing rates and correlations, illustrated here as a sensory variable encoded in the sum of two neural signals ($y_1 + y_2$). Points represent neural activity during a repeated presentation of the same stimulus. Variability orthogonal to this coding axis does not disrupt coding, but could appear as drift in experiments if it occurred on slow timescales. Right: Such distributed codes may be hard to read-out from recorded subpopulations (e.g. $y_1$ or $y_2$ alone; black), especially if they entail correlations between brain areas. (d) Left: External covariates may exhibit context-dependent relationships. Each point here reflects a neural population state at a given time-point. The relationship between directions $x_1$ and $x_2$ changes depending on context (cyan versus red). Middle: Internally, this can be represented a mixture model, in which different subspaces are allocated to encode each context, and the representations are linearly-separable (gray plane). Right: The expanded representation contains two orthogonal subspaces that each encode a separate, context- dependent relationship. This dimensionality expansions increases the degrees of freedom in internal representations, thereby increasing opportunities for drift.

 

Constrained plasticity can compensate for ongoing drift in neural populations

I've started a new postdoc, working on a collaboration between the O'Leary, Ziv, and Harvey labs, on the Human Frontiers Science Program grant, "Building a theory of shifting representations in the mammalian brain". 

To start, I've been working with Adrianna Loback to try to make sense of a puzzling result from Driscoll et al. (2017): the neural code for sensorimotor variables in parietal cortex is unstable, changing dramatically even for habitual tasks in which no learning takes place.

We think the brain might be using a distributed population code. Because there are so many possible ways to read-out a distributed and redundant population code, it could be that there is a stable representation at the population level, despite the apparent instability of single neurons. 

I'll be presenting our work to date as a poster at the UK Neural Computation conference in Nottingham, July 1st-3rd. 

[download poster PDF] 

Abstract:

Recent experiments reveal that neural populations underlying behavior reorganize their tunings over days to weeks, even for routine tasks. How can we reconcile stable behavioral performance with ongoing reconfiguration in the underlying neural populations? We examine drift in the population encoding of learned behaviour in posterior parietal cortex of mice navigating a virtual-reality maze environment. Over five to seven days, we find a subspace of population activity that can partially decode behaviour despite shifts in single-neuron tunings. Additionally, directions of trial-to-trial variability on a single day predict the direction of drift observed on the following day. We conclude that day-to-day drift is concentrated in a subspace that could facilitate stable decoding if trial-to-trial variability lies in an encoding-null space. However, a residual component of drift remains aligned with the task-coding subspace, eventually disrupting a fixed decoder on longer timescales. We illustrate that this slower drift could be compensated in a biologically plausible way, with minimal synaptic weight changes and using a weak error signal. We conjecture that behavioral stability is achieved by active processes that constrain plasticity and drift to directions that preserve decoding, as well as adaptation of brain regions to ongoing changes in the neural code.

This poster can be cited as: 

Rule, M. E., Loback, A. R., Raman, D. V., Harvey, C. D., O'Leary, T. S. (2019) Constrained plasticity can compensate for ongoing drift in neural populations. [Poster] UK Neural Computation 2019, July 1st Nottingham, UK